Ohh, MCQ? This will be easy!

Algebra Level 1

$x+ \dfrac{1}{x}=a+b$ and $x-\dfrac{1}{x}=a-b$

What is the relation between a and b?

Note:-

$x \neq 0$

a=b ab=1 a+b=2

a={b}^{2}

a=2b ab=2 a=3b a+b=0

1 solution

Mehul Arora
Jun 7, 2015

$x+\dfrac{1}{x}=a+b ......(i)$

$x-\dfrac{1}{x}=a-b........(ii)$

Adding (i) and (ii)

2a=2x

$a=x$

Now, $a+\dfrac{1}{a}=a+b$ (Because x=a)

$\dfrac{1}{a}=b$

$ab=1$

Hence, The answer is ab=1.

QED.

Cheers!

It must be mentioned that $x \neq 0$ or it becomes undefined.

Nihar Mahajan - 6 years ago

Done. :) Thanks for Reminding. Again :P

Mehul Arora - 6 years ago